AI Article Synopsis
- The study analyzes how binning neuron spike trains alters their statistical properties, transforming a Markov process into a variable-length Markov chain with infinite memory.
- It establishes that the statistical behavior of these binned spikes can be described using Gibbs measures, providing a new framework for understanding anticipation in neural prediction capabilities.
- Additionally, the research discusses the implications of binning on detecting misleading phase transitions and evidence of criticality in neural data.
Article Abstract
We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process that is no longer Markov but is instead a variable-length Markov chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, that is, to tell "how good" our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future, and we discuss how binning may affect our conclusions on this ability. We finally comment on the possible consequences of binning in the detection of spurious phase transitions or in the detection of incorrect evidence of criticality.
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| http://dx.doi.org/10.1162/NECO_a_00898 | DOI Listing |
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